A vessel of volume 10 liters is filled with $\mathrm{H}_2$ gas. The total average translational kinetic…

A vessel of volume 10 liters is filled with $\mathrm{H}_2$ gas. The total average translational kinetic energy of its molecules is $4.5 \times 10^5 \mathrm{~J}$. The pressure of hydrogen in the vessel is
  1. $3 \times 10^6 \mathrm{Nm}^{-2}$
  2. $30 \times 10^6 \mathrm{Nm}^{-2}$
  3. $30 \times 10^4 \mathrm{Nm}^{-2}$
  4. $3 \times 10^4 \mathrm{Nm}^{-2}$

Solution

Pressure, $P=\frac{2}{3} \frac{\mathrm{E}}{\mathrm{V}}=\frac{2}{3} \times \frac{4.5 \times 10^5}{10 \times 10^{-3}}=30 \times 10^6 \mathrm{Nm}^{-2}$

Asked in: AP EAMCET 2023 (15 May Shift 1)

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